Spectrum spreading of information symbols is a simple method to achieve frequency diversity over a multipath, frequency-selective fading propagation channel, as well as a method for simultaneous multiple-access by a number of users to the same communication channel. Spread-spectrum communication systems with multiple-access capability based on user-specific spreading signatures (also referred to as codes, or sequences) are usually called Code-Division Multiple-Access (CDMA) systems. Multiple-access capability is based on low (ideally zero) cross-correlation between the signatures. Multipath propagation deteriorates the performance of CDMA systems, as the multiple reflections of each signature element result in the distortion of the transmitted signatures. The cross-correlations of the received, distorted signatures deviate from the designed minimized values.
On the other hand, Orthogonal Frequency-Division Multiplexing (OFDM) transmission uses a transmitted cyclic prefix for each block of transmitted symbols to make, in the receiver, the multipath fading channel appear as a single-path channel on each of the orthogonal detected subcarriers. Such a property allows for much simpler receivers than in CDMA systems, when the transmission is over multipath propagation channels. However, by its very nature an OFDM system cannot directly exploit the potential diversity gain of the multipath fading channel.
To make a compromise between the diversity gain and multiple-access capability of CDMA systems, and the receiver simplicity pertained to OFDM systems, so-called MC-CDMA systems have been developed, where n information symbols (possibly obtained after error-correction encoding) are transmitted concurrently (i.e. summed) after spreading and sub-carrier mapping: each information symbol is first multiplied (i.e. spread) by a unique corresponding signature, a sequence of m spreading symbols (chips), and then mapped to a set of m orthogonal sub-carriers, common to all concurrently transmitted information symbols, where each chip of the spread information symbol modulates a dedicated sub-carrier. Finally, the signal obtained by the previous operations is extended by preceding it with the so-called cyclic prefix, which is a block of samples taken from the end of the original signal. In the overloaded case, i.e. the situation where n>m, there are more signature sequences than chips. In this case no orthogonal signature sets exists and interference is inherent.
The operations of sub-carrier mapping and adding the cyclic prefix do not have impact on the properties of Low-Density Spreading (LDS) transmissions on Additive White Gaussian Noise (AWGN) channel. Thus, we shall model the received signal vector r consisting of n received chip-values after passing through a channel, as the following relation:r=Sx+z,   (1),where S is the m×n signature matrix (each signature being a column of this matrix), X is the column vector containing the modulation symbols, and Z is the column vector containing the complex-valued samples of white additive Gaussian noise.
The optimum demodulator for overloaded MC-CDMA transmission is the joint Maximum Likelihood (ML) detection of the set of information symbols transmitted concurrently using different signatures. Such demodulator is typically too complex for practical use, as it has to search through all possible sequences of n information symbols, so a large variety of suboptimal Multiuser Demodulation (MUD) methods have been developed. All suboptimal MUD methods are, in one way or another, approximations of joint ML demodulation.
The MUD receivers are typically still very complex, the complexity increasing non-linearly with the length of signatures. Traditionally, MUD methods have been independent of the signature design, in which case the MUD implementation complexity is dependent only on the number of signatures. It has however recently been demonstrated that the MUD complexity can be reduced by specially designed sparse signatures, accompanied with the usage of Belief Propagation joint Multiuser Demodulation (BP-MUD). If we denote an information symbol modulating a signature as a symbol variable, then the BP-MUD can be described as performing the ML searching on each chip, but only over a (small) set of information symbols that contribute to the energy of each particular chip. That set is defined by the non-zero elements in each row of the LDS signature matrix. Such sparse signatures contain only few chips where the energy is actually transmitted, i.e. each of them has only few non-zero elements. Therefore they are called Low-Density Spreading (LDS) signatures.
An LDS signature of length m is a sequence of m spreading symbols (chips) such that wc chips are not equal to zero, while m-wc are equal to zero, so that wc<<n. The LDS transmission combined, e.g. with OFDM (i.e. LDS-OFDM) is an attractive candidate for future high-capacity wireless communication systems, developed on the foundation of the existing OFDM based global cellular standard (i.e. 3GPP LTE). The concept of LDS-OFDM transmission is shown in FIG. 1 in which LDS spread information symbols are summed into a single vector of length 12 chips, wherein the chips modulate the corresponding subcarriers within an OFDM transmission interval. Further, the FFT processor in FIG. 1 maps frequency domain signal samples into time domain signal samples at its output.
The corresponding BP-MUD demodulator aims at approximating the ML detector by iterating belief values and assumes that the signature matrix S is of the so-called Low-Density Parity-Check (LDPC) type. The BP-MUD demodulator has considerably lower complexity than the ML detector and its performance can be close to that of the MAP detector. The BP-MUD is applicable to any choice of the actual values of the signature sequences.
However, the error rate performances of detected information bits in the receiver do depend on the choice of signature sequences. For example, in noise-free conditions it should be possible to unambiguously detect the information symbols that modulate the different LDS signatures. This is possible only if the modulated signatures represent a Uniquely Decidable (UD) code, as shown in the paper by van de Beek and Popovic from IEEE GLOBECOM 2009 conference.
For the overloaded scenarios, the performance of the system can typically be measured as the gap to the single-user bound (the performance on AWGN channel of a system employing only one user, hence free from inter-user interference). The single-user bound performance can is equivalent to the performance of a CDMA system with load factor 1, using the identity matrix as the signature matrix.
This gap in performance between LDS transmission and the corresponding single user transmission using the same coding and modulation format is mainly a function of the overloading factor and the modulation format (i.e. constellation size) of the information symbols.
The functional block structure of a typical transmitter in a conventional digital wireless communication system is given in FIG. 2. The information bits are grouped in blocks, and each block of information bits is encoded by error correction encoder in order to be protected against additive white Gaussian noise (AWGN) at the receiver. The encoder, for example, a convolutional encoder, produces so-called “mother” code word. The corresponding code rate Rm, defined as the ratio of the number of information bits encoded in a single code word divided by the number of bits in the code word, is called mother code rate. For some applications the code word size has to be adjusted to match available physical resources for the transmission, which is done in the rate matching block, by either puncturing (to shorten the mother code word) or repetition (to extend the mother code word).
Typical and the best error correction codes are designed to protect against the statistically independent errors. For example, such errors occur on AWGN communication channel. However, on fading communication channel, which causes large amplitude variations of the received signal, the received signal amplitude can be below a detection threshold during a number of signalling intervals, resulting in bursts of erroneously received information symbols. Because of that, the errors on the received bits are not statistically independent, and therefore the error correction code designed for AWGN channel would not be capable to effectively protect information on burst-error communication channels.
A simple and effective method for bit error correction on burst-error channels is to use already designed codes for AWGN channels along with an additional functional block, called (channel) bit interleaver, which performs permutation of the bits of each (rate matched) code word. The corresponding inverse permutation of received bits is performed in the channel bit deinterleaver, before error correction decoder. Obviously, the deinterleaver transforms a burst of errors into a disperse pattern of errors. The more disperse error pattern after deinterleaver, the better performances of error correction decoder will be achieved. The optimum bit interleaver for a given code word length is such permutation that makes two successive bits in the permuted code word being at the maximum possible distance before interleaving (counted in number of bit positions between them). Note that on AWGN channel the interleaver and the deinterleaver have no impact on the link performances. Therefore, in the applications where the communication channel is only of AWGN type, the channel bit interleaver and deinterleaver are not used. Therefore the channel bit interleaver in FIG. 2 is denoted as optional.
In FIG. 3, a general receiver block diagram is shown, corresponding to the transmission scheme shown in FIG. 2. The demodulator of FIG. 3 produces soft values of bits transmitted by each information symbol. These soft values are deinterleaved and fed into the error correction decoder, which typically is a convolutional or a turbo decoder in common systems.
The LDS transmission defined up to date is similar to the conventional one, with the only difference in the last stage of the transmitter chain, where LDS Transmitter (Tx) stage is added, to perform spreading and concurrent transmission of multiple information symbols. The functional block structure of the LDS transmitter of the prior art is given in FIG. 4. It should be noted at this point that the channel bit interleaver is optional in the LDS transmitter, meaning that the channel bit interleaver is not used if the communication channel is of AWGN type.
The corresponding state-of-the-art LDS receiver is shown in FIG. 5. The BP-MUD demodulator in FIG. 5 produces soft values (Log Likelihood Ratio—LLR) of the coded bits that are, after deinterleaving (performed only if there is a bit interleaving operation in the transmitter), fed to the error correction decoder. The LLR calculation in BP-MUD demodulator is done once the BP-MUD iterative processing is finished: it uses the final estimated probabilities of all possible symbols from the modulation constellation for each code channel, i.e. for each signature. In other words, the BP-MUD performance is determined by the performance of the estimation of transmitted modulation symbols, meaning that the bits inside these symbols are not directly estimated.
If we denote a modulation symbol modulating a signature as a symbol variable, then the detection of concurrently transmitted modulation symbols is performed in an iterative way, using the sparse connections between the energy of each chip and the subsets of the symbol variables contributing to the energy of each particular chip. These sparse connections are defined by the non-zero elements in each row of the LDS signature matrix.
On the AWGN channel, the connections between each chip and the corresponding symbol variables allow almost ML detection performance of the sequence of n symbol variables transmitted in a LDS transmission interval, but in the same time might be source of a relatively long sequence of erroneously detected symbol variables. The numerical simulations confirmed that it happens indeed, even at high signal-to-noise ratios (SNR) at the receiver: even if the average symbol or bit error rate is quite low, after averaging over a large number of LDS transmission intervals, the instantaneous error rate, obtained as the number of erroneously detected symbols in a single LDS transmission interval, can be rather high—sometimes more than 50% of n concurrently transmitted modulation symbols can be erroneously detected. These erroneous LDS reception intervals are followed by a large number of correct reception intervals, which make the overall, average error rate low.
Such burst-error behaviour of LDS BP-MUD on the AWGN channel seems to be its fundamental inherent property, which is not noticeable when the LDS transmission is without error correction coding, as it that case only the average error rate determines the performance. When the error correction encoding is included in the LDS transmission, the original code word consisting of coded bits is after modulation transformed into a code word of NCWS modulation symbols, where typically NCWS is typically much larger than the number of symbols n that can be transmitted in a single LDS transmission interval. Therefore the code word of modulation symbols has to be cut into NLDS segments, each consisting on n modulation symbols, so that NLDS transmission intervals are needed to send a single code word.
The bursts of errors of LDS BP-MUD, which may occur after reception of some segments of the code word, even on AWGN channel, result in the bursts of erroneous LLRs. The bursts of erroneous LLRs prevent correct functioning of error correction decoders designed for AWGN channels, such as Viterbi and turbo decoders. Consequently, if one compares performances of the LDS transmission to the performances of the conventional communication system on AWGN channel, both either without error correction coding, or with error correction coding, the performance of uncoded LDS transmission is relatively worse than that of coded LDS transmission. In other words, the reduction of the required received SNR which error correction code provide is less pronounced with LDS transmission than in ordinary transmission.
Hence, the error correction coding at the transmitter causes that the gap between the performance of LDS transmission and the performance of conventional transmission, both on AWGN channel, increases compared to the scenario without error correction coding using the same modulation format. The problem is how to modify LDS transmission with error correction coding over AWGN channel in order to minimize the performance gap to the conventional transmission with the same modulation and coding scheme.